MAT4233

Modern Abstract Algebra

MAT 4233. Modern Abstract Algebra. (3-0) 3 Credit Hours.

Prerequisites: MAT3233. Basic properties and examples of semigroups, monoids, and groups, detailed study of permutation, dihedral, and congruence groups, cyclic groups, normal subgroups, quotient groups, homomorphism, isomorphism theorems, direct products of groups, rings and fields and their basic properties, ideals, polynomial rings. Generally offered: Spring. Differential Tuition: $150.

Text

Charles C. Pinter. A Book of Abstract Algebra. (Reprint of 2nd.\ ed.\ originally published in 1990) Dover Publications, NY (2010). ISBN-10: 0-486-47417-8.

Topics

1

Date	Sections	Topics	Student Learning Outcomes
1 and 2	Binary operations on sets.
2	3 and 4	Groups: Definition and elementary properties.
3	5	Subgroups.
4	7 and 8	Groups of Permutations. Permutations of finite sets.
5	9 and 10	Group isomorphisms and orders of elements.
6	---	Review. First midterm exam.
7	11	Cyclic groups.
8	13	Counting cosets.
9	14 and 15	Homomorphisms and quotient groups.
10	---	Review. Second midterm exam.
11	16	The fundamental theorem of homomorphism.
12	17	Rings and ideals.
13	18	Ring homomorphisms.
14	19 and 20	Quotient rings and integral domains.
15	21 and 22	The integers. Factorization into primes.		Wrap-up and review. Student Study Day.